Publication result detail

The Hofmann-Mislove Theorem for general posets

KOVÁR, M.

Original Title

The Hofmann-Mislove Theorem for general posets

English Title

The Hofmann-Mislove Theorem for general posets

Type

Paper in proceedings (conference paper)

Original Abstract

In this paper we attempt to find and investigate the most general class of posets which satisfy a properly generalized version of the Hofmann-Mislove theorem. For that purpose, we generalize and study some notions (like compactness, the Scott topology, Scott open filters, prime elements, the spectrum etc.), and adjust them for use in general posets. Then we characterize the posets satisfying the Hofmann-Mislove theorem by the relationship between the generalized Scott closed prime subsets and the generalized prime elements of the poset. The theory become classic for distributive lattices. Remark that the topologies induced on the generalized spectra in general need not be sober.

English abstract

In this paper we attempt to find and investigate the most general class of posets which satisfy a properly generalized version of the Hofmann-Mislove theorem. For that purpose, we generalize and study some notions (like compactness, the Scott topology, Scott open filters, prime elements, the spectrum etc.), and adjust them for use in general posets. Then we characterize the posets satisfying the Hofmann-Mislove theorem by the relationship between the generalized Scott closed prime subsets and the generalized prime elements of the poset. The theory become classic for distributive lattices. Remark that the topologies induced on the generalized spectra in general need not be sober.

Key words in English

Posets, generalized Scott topology, Scott open filters, (filtered) compactness, saturated sets, prime elements, prime subsets

Authors

KOVÁR, M.

RIV year

2011

Released

14.10.2004

Publisher

IBFI Schloss Dagstuhl

Location

Schloss Dagstuhl, Deutschland

Book

Proceedings of the Dagstuhl Seminar 04351 - Spatial Representation: Discrete vs. Continuous Computational Models

Volume

1

Number

04351

Pages from

1

Pages count

16

URL

ftp://ftp.dagstuhl.de/pub/Proceedings/04/04351/04351.KovarMartin3.Paper!.pdf

BibTex

@inproceedings{BUT11709,
  author="Martin {Kovár}",
  title="The Hofmann-Mislove Theorem for general posets",
  booktitle="Proceedings of the Dagstuhl Seminar 04351 - Spatial Representation: Discrete vs. Continuous Computational Models",
  year="2004",
  volume="1",
  number="04351",
  pages="16",
  publisher="IBFI  Schloss Dagstuhl",
  address="Schloss Dagstuhl, Deutschland",
  url="ftp://ftp.dagstuhl.de/pub/Proceedings/04/04351/04351.KovarMartin3.Paper!.pdf"
}